Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography [PDF]
, 2021 This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. Specifically, we introduce the so-called semilinear transformations in coding theory and then apply them to the construction of code ...
Wenshuo Guo, Fang-Wei Fu
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Jump to Conclusions: Short-Cutting Transformers with Linear Transformations [PDF]
International Conference on Language Resources and Evaluation, 2023 Transformer-based language models create hidden representations of their inputs at every layer, but only use final-layer representations for prediction.
Alexander Yom Din +3 more
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Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks [PDF]
Advanced Photonics Nexus, 2023 . As an optical processor, a diffractive deep neural network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through ...
Xilin Yang +4 more
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Polarization multiplexed diffractive computing: all-optical implementation of a group of linear transformations through a polarization-encoded diffractive network [PDF]
Light: Science & Applications, 2022 Research on optical computing has recently attracted significant attention due to the transformative advances in machine learning. Among different approaches, diffractive optical networks composed of spatially-engineered transmissive surfaces have been ...
Jingxi Li +4 more
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Massively parallel universal linear transformations using a wavelength-multiplexed diffractive optical network [PDF]
Advanced Photonics, 2022 . Large-scale linear operations are the cornerstone for performing complex computational tasks. Using optical computing to perform linear transformations offers potential advantages in terms of speed, parallelism, and scalability.
Jingxi Li +3 more
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Apartments preserving transformations of Grassmannians of infinite-dimensional vector spaces [PDF]
, 2017 We define the Grassmannians of an infinite-dimensional vector space V as the orbits of the action of the general linear group GL ( V ) on the set of all subspaces. Let G be one of these Grassmannians.
M. Pankov
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Remarks on the classification of a pair of commuting semilinear operators [PDF]
, 2011 Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl.
Debora Duarte de Oliveira +3 more
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On geometry of linear involutions [PDF]
, 2005 Let $V$ be an $n$-dimensional left vector space over a division ring $R$ and $n\ge 3$. Denote by ${\mathcal G}_{k}$ the Grassmann space of $k$-dimensional subspaces of $V$ and put ${\mathfrak G}_{k}$ for the set of all pairs $(S,U)\in {\mathcal G}_{k ...
M. Pankov
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Arbitrary linear transformations for photons in the frequency synthetic dimension [PDF]
Nature Communications, 2020 Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning.
Siddharth Buddhiraju +4 more
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Universal linear intensity transformations using spatially incoherent diffractive processors [PDF]
Light: Science & Applications, 2023 Under spatially coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number ( N ) of ...
Md. Sadman Rahman +4 more
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